Mathematical model and undercutting of cylindrical gears with curvilinear shaped teeth

The Equation of the Contact Line of the Involute Curvilinear-Tooth Cylindrical Gear Pump for the Agricultural Tractor

“…R b1 and R b2 symbolize the radii of the base cylinders of the two gears respectively. w (1) and w (2) denote the angular velocity of the two gears respectively. Point m (1) and m (2) , located at the tooth surface ∑ 1 and ∑ 2 , contact at the point m. No.1 gear and No.2 gear rotate through an angle β 1 and β2 respectively from their initial position.…”

“…w (1) and w (2) denote the angular velocity of the two gears respectively. Point m (1) and m (2) , located at the tooth surface ∑ 1 and ∑ 2 , contact at the point m. No.1 gear and No.2 gear rotate through an angle β 1 and β2 respectively from their initial position. Now if the two gears are cut apart across point m, then their intersection can be illustrated by As shown by Fig.…”

“…But the teeth on the base cylinder of the gear are curvilinear shaped. Researches about the curvilinear-tooth gear are continually conducted [2][3][4][5][6][7]. In this study, the tooth surface of the involute curvilineartooth gear is firstly generated as that of the spur or helical gear; then the equation of the tooth surface and the meshing equation are derived; and finally the equation of the contact line is calculated.…”

Modal Analysis of Cylindrical Gears with Arcuate Tooth Trace

“…So, the Japanese scholars, Kazuo Inoue successively have proposed finish machining method such as grinding teeth and burnishing teeth. Because of long contact line, high contact ratio, smooth transmission, high bearing capacity, good lubrication performance and a serial of advantages, cylindrical gears with arcuate tooth trace has been researched by many scholars all over the world [1][2][3][4][5][6][7][8][9][10]. Thus, there are many difficult with the processing and design, the cylindrical gears with arcuate tooth trace has not been widely applied [2][3].…”

“…Tseng has built mathematical model of arc gear, but not studied its bending characteristics with his partners and Wilcox et al have made different gears' stress analysis by finite method, but they don't specifically research that how the important parameters such as tooth line radius influence [4][5][6][7]. Professor Chen-min has made some breakthrough in analysis of arc gear forming principle, meshing performance and carrying capacity, but the modal was not analyzed [8][9].…”